Title: Modeling the Public Health Impact of E-Cigarettes on Adolescents and AdultsAuthors: Lucia Wagner and Sara Clifton, St. Olaf College, Northfield, MN 55057Abstract: Since the introduction of electronic cigarettes to the United States market in 2007, vaping prevalence has surged in both adult and adolescent populations. E-cigarettes are advertised as a safer alternative to traditional cigarettes and as a method of smoking cessation, but the U.S. government and health professionals are concerned that e-cigarettes attract young non-smokers.  Here, we develop and analyze a dynamical systems model of competition between traditional and electronic cigarettes for users. With this model, we predict the change in smoking prevalence due to the introduction of vaping, and we determine the conditions under which e-cigarettes present a net public health benefit or harm to society.Files included in project directory:- LW_adult_fit_ACEmodel- LW_youth_fit_ACEmodel- PrevalenceHistogram- SensitivityAnalysis- shadedErrorBarData included in project directory:- smoking_data (NOTE: adult data obtained from CDC and Lang et al.)- YouthSmokingData (NOTE: adolescent data obtained from CDC)Purpose of files and data:- LW_adult_fit_ACEmodel: Fits the ACE (abstain-cigarette-e cigarette) model to adult data obtained from the CDC, plotting time (in real years) versus ACE populations and time (in real years) versus public health ratio (r). Generates figures 3, 5, and 6.- LW_youth_fit_ACEmodel: Fits the ACE (abstain-cigarette-e cigarette) model to adolescent data obtained from the CDC, plotting time (in real years) versus ACE populations and time (in real years) versus public health ratio (r). Generates figures 4, 5, and 6.- PrevalenceHistogram: Plots time (in real years) versus cigarette and e-cigarette prevalence data obtained from the CDC for both adults and adolescents. Generates figure 2.- SensitivityAnalysis: Plots vaping utility inflection year (TE) versus public health ratio (r) and maximum vaping prevalence, serving as a sensitivity analysis of TE. Generates figure 7. - shadedErrorBar: Adds average residual to figures 3 and 4.- smoking_data: Adult cigarette and e-cigarette prevalence data obtained from the CDC and Lang et al.- YouthSmokingData: Adolescent cigarette and e-cigarette prevalence data obtained from the CDC.How to run code:- Step 1: Download data files (.mat) to MATLAB- Step 2: Download code files (.m) to MATLAB- Step 3: Run code files in MATLAB- Click 'Editor'- Click 'Run'- NOTE: each file annotated with particular functionalityThese files were developed and tested on R2020a and R2019b.Details on manuscript figures generated in MATLAB:- Figure 2: PrevalenceHistogramEnsure adult and adolescent data files are downloaded into MATLAB. Click �Run�.- Figure 3: LW_adult_fit_ACEmodelEnsure the adult data file is downloaded into MATLAB. Adjust the �tend� variable, specifying the end year of the simulation (end of data, or longer). Adjust the �tipE� variable, specifying the projected vaping utility inflection year (TE). Click �Run�. - Figure 4: LW_youth_fit_ACEmodelEnsure the adolescent data file is downloaded into MATLAB. Adjust the �tend� variable, specifying the end year of the simulation (end of data, or longer). Adjust the �tipE� variable, specifying the projected vaping utility inflection year (TE). Click �Run�.- Figure 5: LW_adult_fit_ACEmodel/LW_youth_fit_ACEmodelEnsure the adult or adolescent data file is downloaded into MATLAB. Adjust the �tend� variable, specifying the end year of the simulation (end of data, or longer). Adjust the �tipE� variable, specifying the projected vaping utility inflection year (TE). Click �Run�. Please refer to the manuscript for a detailed description of the public health ratio (r).- Figure 6: LW_adult_fit_ACEmodel/LW_youth_fit_ACEmodelEnsure the adult or adolescent data file is downloaded into MATLAB. Adjust the �tend� variable, specifying the end year of the simulation (end of data, or longer). Adjust the �tipE� variable, specifying the projected vaping utility inflection year (TE). The figure is dependent on tipE. Click �Run�. Please refer to the manuscript for a detailed description of the sensitivity analysis.- Figure 7: SensitivityAnalysis/LW_adult_fit_ACEmodel/LW_youth_fit_ACEmodelEnsure the adult or adolescent data file is downloaded into MATLAB. For the LW_adult_fit_ACEmodel/LW_youth_fit_ACEmodel files, adjust the �tipE� variable, specifying the projected vaping utility inflection year (TE). Click �Run�. Ensure the line �max(Y_rw(:,2))� is unsuppressed to generate the maximum vaping prevalence. Ensure the line �desiredY = interp1(t(10:end),r(10:end),2030)� is unsuppressed to generate the public health ratio (r) in 2030. The year can be altered to extract the public health ratio (r) for any desired year. Click �Run�. Output values were included in the SensitivityAnalysis file to understand trends in maximum vaping prevalence and public health ratio (r) over time. Please refer to the manuscript for a detailed description of the sensitivity analysis.Details on manuscript results generated in MATLAB:- Peak prevalence of cigarettes and e-cigarettesInterpolation extracted from fitting the ACE (abstain-cigarette-e cigarette) model to adult and adolescent data obtained from the CDC (and also Lang et al. for adults) using the pseudocode: maximum prevalence = max(model prevalence data, either cigarettes or e-cigarettes)- Average prevalence of smokers diverted by vapingThe difference between the areas under the counterfactual model and real life smoking model curves (post-vaping), averaged over years. Used MATLAB �trapz� function to execute code.- Public health ratio: if the health risk of smoking is X times worse than vaping, e-cigarettes present a net benefit for public healthInterpolation extracted from the public health ratio (r) figure using the pseudocode: ratio r = interp1(time vector, ratio of vaping to smoking difference per time, year in question)- Average residualThe absolute value of the difference between the model and the data, averaged over all years.Credits: The authors thank Gabby Digan, Ruiyi Wang, and Elizabeth Wei for contributions to early  exploration  of  the  model.  Thanks  are  also  due  to  the  Illinois  Geometry  Lab and Mathways Grant No. DMS-1449269 (SMC) for research support.Please direct questions/comments to:Sara Cliftonclifto2@stolaf.edu